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Communications in Mathematical Physics

, Volume 330, Issue 3, pp 1155–1178 | Cite as

Stability of Asymptotics of Christoffel–Darboux Kernels

  • Jonathan BreuerEmail author
  • Yoram Last
  • Barry Simon
Article

Abstract

We study the stability of convergence of the Christoffel–Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under 1 and random 2 diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.

Keywords

Orthogonal Polynomial Continuous Spectrum Jacobi Matrice Random Matrix Theory Orthogonality Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael
  2. 2.Mathematics 253-37California Institute of TechnologyPasadenaUSA

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